WP(extra point) vs. WP(2-pt make)*.4 + WP(2-pt miss)*.6
I think this is the crux of my argument. My assumption is that WP(extra point) is higher.]
In the wake of Michigan's loss to Iowa, game theorists are criticizing Brady Hoke's decision to kick the extra point rather than go for two on Michigan's fourth-quarter scoring drive. Though I know it goes against traditional game theory to kick the extra point, I can't shake the feeling that it was the correct decision.
Hear me out. Michigan scored to make the game 15-24 with 7:53 remaining on the clock. Game theory states that Michigan should go for the two-point conversion because, if they miss, it will inform the coaches whether or not they need one or two scores with the remaining time, and can adjust their playcalling accordingly. But there's one play that this theory doesn't take into account: a successful, expected onside kick.
First, let's examine the path to victory that Michigan would have to follow for all of the possible scenarios (with the exception of missing the extra point because, well, if you do that twice in a game, shame on you):
| Go for 1 | Go for 2 make | Go for 2 miss |
| Defensive stop | Defensive stop | Defensive stop |
| Touchdown drive | Touchdown drive | Touchdown drive |
| 2-point conversion | Extra point | Extra point |
| Overtime | Overtime | Expected onside kick recovery |
| Field goal drive |
Michigan, obviously, elected to kick the extra point. With that decision, the team was essentially playing for a coin flip (2-point conversions are successful about 40% of the time). Kicking off with 7:53 remaining, Michigan needed a defensive stop as well as a successful touchdown drive and two-point conversion. As the game played out, Michigan had ample time for that. Not only did the defense force a stop after 2:41, but they were able to fit in two more drives and a second defensive stop (offensive drives consisted of: 1:13 off the clock preceding a punt, and 2:15 off the clock ebfore stalling at the 3 yard line; the second defensive stop took 1:44). Had they been able to punch the ball into the endzone, they would've had a 40% chance of tying the game and sending it into overtime. From there, it's anyone's game.
If Michigan makes the two-point conversion, the same scenario unfolds as above, but instead of needing a two-point conversion after the possible tying touchdown they only need an extra point. There is ample time for this situation, and it is the best-case scenario.
The problem lies in missing the two-point conversion early in the quarter. If Michigan had gone for the two-point conversion and missed, it's a two-possession game (9 points) with 7:53 to go. In that instance, not only does Michigan have to force a defensive stop (which they do), but also receive the ball, march down for a score, successfully complete an onside kick (about which more later), and drive for another score. Not only does the successful completion of an onside kick present problems, but time then becomes a major factor.
Hypothetically, let's say that Michigan scores with 7:53 left in the game and misses its two-point conversion attempt. They're down nine, kicking off, and need two scores. If the defense produces the identical defensive stop, they will receive the ball on their own four yard line with 5:12 remaining. Michigan's fastest scoring drive of the day was its final one, which covered 57 yards and took 2:49 (0.337 yards/second). If Michigan continued that pace, a drive of 96 yards would take them 4:44. If we're generous and shave off a minute from that time, Michigan is left with 1:28 and probably zero timeouts. In that time, they have to successfully recover an onside kick and move the ball about 35-40 yards to have a makeable field goal for the win.
While this is doable, onside kicks present a huge gamble. According to Advanced NFL Stats (caveats about these being NFL numbers apply, but only barely),
Onside kicks in the NFL are successful 26% of the time. It’s true, but it’s also very misleading. Onside kick success rates are very dependent on whether the receiving team is expecting one...In this situation, Iowa would be expecting an onside kick, making the success rate somewhere at or near 20%. With a true freshman kicker who has never attempted a collegiate onside kick? Michigan's chances would be low.
When teams are expecting it, when WP is about 0.15 and below, the success rate is about 20%. But when teams aren’t expecting it, the success rate averages 60%.
The point is that going for two points earlier in the quarter, while it would pay off significantly if you convert (40%) basically puts the game out of reach if you fail (60%). Not only does clock management become a significant issue if you miss the two-point conversion early, but Hoke would also be asking his team to play nearly perfect football for close to 8 minutes. With Michigan's current team, that's asking too much.
This is why I feel like the "information" angle of game theory here is short-sighted. Would Michigan's coaches know whether or not they needed two scores? Sure, but getting two scores in that time-frame while playing errorless football is the equivalent of putting the game out of reach. By kicking the extra point, Michigan creates a potentially one-score game and forces Iowa to play errorless football (a fumble or interception changes the game significantly). Most importantly, it removes the variance of a successful, expect onside kick.
As it played out, if Michigan was able to score, that gives them a 40% chance of taking the game to overtime. But that same 40% chance of making the two-point conversion earlier in the quarter significantly increases the win variance and Michigan's ability to convert what is needed for an eventual victory. So while kicking the extra point may not make the game a guaranteed one-score game, it does indicate that you're playing for one more scoring drive. Because with the time remaining, playing for two is nearly impossible.
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